To simplify the expression 1/2(x+4)+1/4(4x-2), we can distribute and combine like terms.
1/2(x+4) = 1/2*x + 1/2*4 = 1/2*x + 2
1/4(4x-2) = 1/4*4x - 1/4*2 = x - 1/2
Putting both simplified terms back into the expression:
1/2(x+4)+1/4(4x−2) = 1/2*x + 2 + x - 1/2
Combining like terms:
= 1/2*x + x + 2 - 1/2
= (1/2*x + x) + (2 - 1/2)
= 3/2*x + 3/2
Expressing the answer in mixed number form:
3/2 can be rewritten as 1 1/2.
Therefore, the expression 1/2(x+4)+1/4(4x−2) in mixed number form is 1 1/2*x + 1 1/2.
Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.(1 p
14 answers
can i get a clearer answer
Certainly! Here's a clearer answer:
To simplify the expression 1/2(x+4)+1/4(4x-2), we can distribute and combine like terms.
First, let's simplify 1/2(x+4):
1/2(x+4) = 1/2 * x + 1/2 * 4
= 1/2x + 2
Now, let's simplify 1/4(4x-2):
1/4(4x-2) = 1/4 * 4x - 1/4 * 2
= x - 1/2
Now, putting both simplified terms back into the expression:
1/2(x+4)+1/4(4x−2) = 1/2x + 2 + x - 1/2
Next, let's combine like terms:
= (1/2x + x) + (2 - 1/2)
= 1/2x + x + 2 - 1/2
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 2.
= (1/2 * 2/2)x + (2 * 2/2) + (1 * 2/2) - (1/2 * 2/2)
= (2/4)x + 4/2 + 2/2 - 1/4
= (2/4)x + 8/4 + 2/4 - 1/4 (combining all terms with the common denominator)
= (2x + 8 + 2 - 1)/4
= (2x + 9)/4
So, the expression 1/2(x+4)+1/4(4x−2) simplifies to (2x + 9)/4.
To simplify the expression 1/2(x+4)+1/4(4x-2), we can distribute and combine like terms.
First, let's simplify 1/2(x+4):
1/2(x+4) = 1/2 * x + 1/2 * 4
= 1/2x + 2
Now, let's simplify 1/4(4x-2):
1/4(4x-2) = 1/4 * 4x - 1/4 * 2
= x - 1/2
Now, putting both simplified terms back into the expression:
1/2(x+4)+1/4(4x−2) = 1/2x + 2 + x - 1/2
Next, let's combine like terms:
= (1/2x + x) + (2 - 1/2)
= 1/2x + x + 2 - 1/2
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 2.
= (1/2 * 2/2)x + (2 * 2/2) + (1 * 2/2) - (1/2 * 2/2)
= (2/4)x + 4/2 + 2/2 - 1/4
= (2/4)x + 8/4 + 2/4 - 1/4 (combining all terms with the common denominator)
= (2x + 8 + 2 - 1)/4
= (2x + 9)/4
So, the expression 1/2(x+4)+1/4(4x−2) simplifies to (2x + 9)/4.
Add: (4d−3)+(12d+4) .
To add (4d-3) and (12d+4), we simply combine like terms:
(4d-3) + (12d+4) = 4d + 12d - 3 + 4
Combining the 4d and 12d terms gives us 16d:
= 16d - 3 + 4
Now we can simplify the constants:
= 16d + 1
So, the sum of (4d-3) and (12d+4) is 16d + 1.
(4d-3) + (12d+4) = 4d + 12d - 3 + 4
Combining the 4d and 12d terms gives us 16d:
= 16d - 3 + 4
Now we can simplify the constants:
= 16d + 1
So, the sum of (4d-3) and (12d+4) is 16d + 1.
Add: (2m−3)+(3n−1)+(3m+1) .
To add (2m-3), (3n-1), and (3m+1), we combine like terms:
(2m-3) + (3n-1) + (3m+1)
First, let's combine the terms with "m":
= 2m + 3m - 3 + 1
Simplifying the "m" terms:
= 5m - 2
Now let's combine the constant terms:
= 5m - 2 - 3
Simplifying the constants:
= 5m - 5
So, the sum of (2m-3), (3n-1), and (3m+1) is 5m - 5.
(2m-3) + (3n-1) + (3m+1)
First, let's combine the terms with "m":
= 2m + 3m - 3 + 1
Simplifying the "m" terms:
= 5m - 2
Now let's combine the constant terms:
= 5m - 2 - 3
Simplifying the constants:
= 5m - 5
So, the sum of (2m-3), (3n-1), and (3m+1) is 5m - 5.
Subtract: 2(10b+4)−(b−2).
To subtract 2(10b+4) - (b-2), we distribute and combine like terms:
First, let's distribute the 2 to (10b+4):
= 2 * 10b + 2 * 4 - (b-2)
= 20b + 8 - (b - 2)
Next, let's remove the parenthesis by distributing the negative sign:
= 20b + 8 - b + 2
Now, let's combine the "b" terms and the constants:
= (20b - b) + (8 + 2)
= 19b + 10
So, the result of 2(10b+4) - (b-2) is 19b + 10.
First, let's distribute the 2 to (10b+4):
= 2 * 10b + 2 * 4 - (b-2)
= 20b + 8 - (b - 2)
Next, let's remove the parenthesis by distributing the negative sign:
= 20b + 8 - b + 2
Now, let's combine the "b" terms and the constants:
= (20b - b) + (8 + 2)
= 19b + 10
So, the result of 2(10b+4) - (b-2) is 19b + 10.
Subtract: (3g−4)−2(3g+4).
To subtract (3g-4) - 2(3g+4), we first distribute the -2 to (3g+4):
= 3g - 4 - 2 * 3g - 2 * 4
= 3g - 4 - 6g - 8
Next, let's combine like terms:
= (3g - 6g) + (-4 - 8)
= -3g - 12
Thus, the result of (3g-4) - 2(3g+4) is -3g - 12.
= 3g - 4 - 2 * 3g - 2 * 4
= 3g - 4 - 6g - 8
Next, let's combine like terms:
= (3g - 6g) + (-4 - 8)
= -3g - 12
Thus, the result of (3g-4) - 2(3g+4) is -3g - 12.
may I have all of the answers in the correct order, please?
Certainly! Here are the answers to the problems in the correct order:
1. Addition: (4d-3) + (12d+4) simplifies to 16d + 1.
2. Addition: (2m-3) + (3n-1) + (3m+1) simplifies to 5m - 5.
3. Subtraction: 2(10b+4) - (b-2) simplifies to 19b + 10.
4. Subtraction: (3g-4) - 2(3g+4) simplifies to -3g - 12.
Please let me know if there's anything else I can help you with!
1. Addition: (4d-3) + (12d+4) simplifies to 16d + 1.
2. Addition: (2m-3) + (3n-1) + (3m+1) simplifies to 5m - 5.
3. Subtraction: 2(10b+4) - (b-2) simplifies to 19b + 10.
4. Subtraction: (3g-4) - 2(3g+4) simplifies to -3g - 12.
Please let me know if there's anything else I can help you with!
number 2 is wrong